The invention more specifically relates to a method that enhances the resolution of a seismic image obtained using inversion algorithms.
Geological surveys often use seismic waves that propagate through a geological medium between a seismic wave emitter and a receiver. The seismic data thus obtained corresponds, at each detector, to seismic wave amplitudes as a function of time. To obtain a three-dimensional information on the composition of the geological medium, geological surveys measure multi-offset seismic data. In such multi-offset seismic data, a plurality of emitters and detectors is used, so that each emitted wave echoing from a reflector in the geological medium is perceived by different detectors, each detector being offset by a certain distance from the emitter. These apparent redundancies in seismic data provide valuable information regarding the reliability of a model of the geological medium constructed to fit this data.
In order to visualize the composition of the geological medium, this time-dependent data needs to be converted into depth-dependent data, where each echo corresponds to an interface called reflector or “seismic horizon”. To obtain a seismic image from this data, a method called seismic tomography analyses the different arrival times of seismic waves and extracts information relating to velocities of waves through the medium. A seismic image therefore comprises a multitude of layers in the geological medium. Each layer corresponds to a medium having specific rheological properties.
If the rheological properties of the geological medium are known, notably the seismic wave velocities in that medium, it is possible to obtain a seismic image from the time-dependent data using a transformation called migration. The redundancy of the multi-offset seismic data can be used to check the reliability of the model by plotting butterfly diagrams in representations called “Common Image Gathers” (CIG), which represent the position of a point of a seismic horizon along a vertical axis corresponding to depth, as a function of the offset between an emitter and a receiver. If the depth of that point as a function of offset remains constant, the velocity model at that horizon is correct. If however, that depth increases or decreases as a function of the offset, it is an indication that the velocity is respectively too low or too high.
Seismic tomography can be seen in mathematical terms as an inverse problem comprising billions of linear equations involving hundreds of millions of unknowns. In ray-based tomography, these equations comprise unknowns among the rheological properties of the geological medium, for instance seismic wave velocities in the medium, and the position and shape of the seismic horizons at which waves reflect. Given the enormous amount of seismic data collected during a geological survey, no reliable method can solve these equations within an acceptable time frame while also providing precise enough solutions.
One possibility is to solve the inverse problem by using matrix methods such as a Cholesky decomposition. Nonetheless, such a matrix-based approach is tremendously demanding in computation power and memory storage.
Other methods involve iterative approaches. Among the most notorious iterative approaches, the Krylov method solves the system equation by equation. Nevertheless, this method requires many iterations, up to millions of iterations per equation, to converge towards a precise enough solution.
Generally, seismic inversion algorithms are designed to accept gross approximations which require fewer iterations, no more than a hundred and therefore provide images with fewer details, resulting in a lower resolution. Sadly, a lot of useful information that is contained in the fine details corresponding to small eigenvalues in a matrix representation of the data is lost. More specifically, vertical resolution is lost with a small number of iterations.
One common iterative approach using seismic tomography techniques to obtain a seismic image is called “Migration Velocity Analysis” (hereafter MVA). Starting from an initial velocity profile, which can be a random approximation of the expected velocities, migration velocity analysis involves four steps performed iteratively: provide a velocity profile, migrate the seismic data to obtain a seismic image, apply a residual move out algorithm, for example on common image gathers, to obtain correction factors of the velocity at several points of the image, and apply and inversion algorithm to obtain an updated velocity profile based on these corrected factors. For example, a Dix inversion algorithm or variations thereof are commonly used.
Another approach to increase the convergence towards a realistic velocity profile consists in manually picking horizons on a seismic image to fix points and simplify the inverse problem. Nevertheless, manually picking horizons is a tedious task which is also prone to human errors. It cannot be automatically implemented in a systematic way to pick a number of horizons providing realistic results using simplified inversion algorithms involving MVA. Sometimes, picking the horizons can be facilitated by orienting horizons along the dip on a seismic image. Nevertheless, these methods involve manual picks which fail to overcome the drawback of human intervention.
Therefore, due to the problems of gross iteration algorithms resulting in lower resolutions, and the lack of automated procedures to implement MVA using simplified inversion algorithms, a method that would allow an enhancement of the resolution of a seismic image is sought.